Estimating the boundary surface between geologic formations from 3D seismic data using neural networks and geostatistics

The exact locations of horizons that separate geologic sequences are known only at physically sampled locations (e.g., borehole intersections), which, in general, are very sparse. 3D seismic data, on the other hand, provide complete coverage of a volume of interest with the possibility of detecting the boundaries between formations with, for example, contrasted acoustic impedance. Detection of boundaries is hampered, however, by coarse spatial resolution of the seismic data, together with local variability of acoustic impedance within formations. The authors propose a two-part approach to the problem, using neural networks and geostatistics. First, an artificial neural network is used for boundary detection. The training set for the neural net comprises seismic traces that are collocated with the borehole locations. Once the net is trained, it is applied to the entire seismic grid. Second, output from the neural network is processed geostatistically to filter noise and to assess the uncertainty of the boundary locations. A physical counterpart is interpreted for each structure inferred from the spatial semivariogram. Factorial kriging is used for filtering, and uncertainty in the shape of the boundaries is assessed by geostatistical simulation. In this approach, the boundary locations are interpreted as random functions that can be simulated to incorporate their uncertainty in applications. A case study of boundary detection between sandstone and breccia formations in a highly faulted zone is used to illustrate the methodologies. Manuscript received by the Editor June 12, 2003; revised manuscript received June 14, 2004; published online January 14, 2005. 1University of Adelaide, Faculty of Engineering, Computer and Mathematical Sciences, Adelaide, South Australia 5005, Australia. E-mail: [email protected]. 2University of Leeds, Department of Mining and Mineral Engineering, Leeds LS2 9JT, United Kingdom. E-mail: [email protected]. c © 2005 Society of Exploration Geophysicists. All rights reserved. INTRODUCTION Many engineering applications, including hydrocarbon reservoir production, mineral extraction, tunneling, and underground storage or disposal of hazardous wastes, require characterization of the geology of the subsurface of the earth. Usually, in these applications, at least in the planning stages, the only direct access to subsurface geology is provided by boreholes, which must be kept to a minimum for economic and/or physical reasons. 3D seismic data on the other hand, provide a nonintrusive source of information that has more complete coverage of the volume of interest. One of the most important structural features that can be extracted from seismic data is the spatial position of distinctive geological formations (as inferred from, for example, acoustic impedance). The precise locations of the boundary surfaces of horizons that separate geologic formations are often of critical importance in engineering applications. The position of these boundaries is known with accuracy only at sparse borehole locations. 3D seismic data provide a much more complete spatial coverage than borehole data, but they yield significantly less accurate information about boundary locations, largely because: 3D data are indirect measurements (e.g., traces of seismic amplitudes or acoustic impedances) from which the value of the direct variable (boundary location) must be inferred. Seismic data are essentially proxies for the boundary locations, As seismic waves travel downward, their frequency is selectively filtered by various geologies; thus, only structural features above a certain size will affect the waves and be registered by the recording geophones. Because the boundary positions are known exactly at the borehole intersections, they can also be tracked precisely in